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Semiparametric estimation of Markov decision processes with continuous state space

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  • Srisuma, Sorawoot
  • Linton, Oliver

Abstract

We propose a general two-step estimator for a popular Markov discrete choice model that includes a class of Markovian games with continuous observable state space. Our estimation procedure generalizes the computationally attractive methodology of Pesendorfer and Schmidt-Dengler (2008) that assumed finite observable states. This extension is non-trivial as the policy value functions are solutions to some type II integral equations. We show that the inverse problem is well-posed. We provide a set of primitive conditions to ensure root-T consistent estimation for the finite dimensional structural parameters and the distribution theory for the value functions in a time series framework.

Suggested Citation

  • Srisuma, Sorawoot & Linton, Oliver, 2012. "Semiparametric estimation of Markov decision processes with continuous state space," Journal of Econometrics, Elsevier, vol. 166(2), pages 320-341.
  • Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:320-341
    DOI: 10.1016/j.jeconom.2011.10.003
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    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    2. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    3. Chen, Xiaohong & Pouzo, Demian, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Working Papers 38, Yale University, Department of Economics.
    4. Sumru Altuğ & Robert A. Miller, 1998. "The Effect of Work Experience on Female Wages and Labour Supply," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 45-85.
    5. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    6. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 265-289.
    7. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    8. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    9. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    11. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January.
    12. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, September.
    13. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    14. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    15. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    16. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    17. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    18. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    19. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    20. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    21. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    22. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    23. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    24. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
    25. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    26. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    27. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
    28. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729 Elsevier.
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    Cited by:

    1. Taisuke Otsu & Martin Pesendorfer & Yuya Takahashi, 2016. "Pooling data across markets in dynamic Markov games," Quantitative Economics, Econometric Society, vol. 7(2), pages 523-559, July.
    2. Armstrong, Timothy B. & Bertanha, Marinho & Hong, Han, 2014. "A fast resample method for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 179(2), pages 128-133.
    3. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    4. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.

    More about this item

    Keywords

    Discrete Markov decision models; Kernel smoothing semiparametric estimation; Well-posed inverse problem;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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